Surprise! The Hubble Constant Changes Over Time

A portion of the Hubble eXtreme Deep Field in full UV-vis-IR light, the deepest image ever obtained. The different galaxies shown here are at different distances and redshifts, and allow us to derive Hubble's law.NASA, ESA, H. Teplitz and M. Rafelski (IPAC/Caltech), A. Koekemoer (STScI), R. Windhorst (Arizona State University), and Z. Levay (STScI)

The Universe is an enormous place, filled with stars and galaxies for billions of light years in all direction. Ever since the Big Bang, light has been traveling from every source that's created it, with a tiny fraction eventually arriving at our eyes. But the light doesn't simply propagate through the space between where its emitted and where we are today; the fabric of space itself is expanding.

The farther away a galaxy is, the more the expansion of space stretches — and therefore, redshifts — the light that will eventually arrive at our eyes. As we look to greater and greater distances, we see redshifts that increase. If we plot out how this apparent recession speed scales with distance, we get a nice, straight-line relationship: Hubble's law. But the slope of that line, known as Hubble's constant, isn't actually a constant at all. It's one of the biggest misconceptions in all of astronomy.

The redshift-distance relationship for distant galaxies. The points that don't fall exactly on the line owe the slight mismatch to the differences in peculiar velocities, which offer only slight deviations from the overall observed expansion. The original data from Edwin Hubble, first used to show the Universe was expanding, all fit in the small red box at the lower-left.Robert Kirshner, PNAS, 101, 1, 8-13 (2004)

There are two ways that we understand the Universe's expansion: theoretically and observationally. When we look out at the Universe, we see a number of important facts about the expansion:

the Universe expands at the same rate in all directions,

the more distant a galaxy is, the faster it recedes from us,

and that this is only true on average.

When we look at individual galaxies, there are large discrepancies in the speeds they actually have, and this is due to gravitational interactions of everything else in the entire Universe.

A two-dimensional slice of the overdense (red) and underdense (blue/black) regions of the Universe nearby us. The lines and arrows illustrate the direction of peculiar velocity flows, but all of this is embedded in a fabric of expanding space.Cosmography of the Local Universe — Courtois, Helene M. et al. Astron.J. 146 (2013) 69

But this is not an insurmountable problem. The Universe is not a place where we only have a few galaxies we can measure the redshift and distance to; there are literally millions of galaxies that we've done this for. As we find a huge slew of galaxies, we can do what's called "binning" them together, where we'll take galaxies in a certain distance range and average them together, calculating an average redshift for them. As we do this, we find that straight-line relation that defines Hubble's law.

Here's the surprise, though. If we look to large enough distances, we can see that the expansion rate no longer follows that straight-line law, but rather curves.

A plot of the apparent expansion rate (y-axis) vs. distance (x-axis) is consistent with a Universe that expanded faster in the past, but is still expanding today. This is a modern version of, extending thousands of times farther than, Hubble's original work. Note the fact that the points do not form a straight line, indicating the expansion rate's change over time.Ned Wright, based on the latest data from Betoule et al. (2014)

When we use a term like "the Hubble constant," we're talking about the slope of that line. If it's not a line — i.e., if the slope changes — that tells us that the Hubble expansion rate of the Universe isn't truly a constant after all! The reason we call it the Hubble constant is because the Universe expands at the same rate at every location in the Universe: the Hubble constant is constant throughout space.

But the expansion rate, and therefore the value of the Hubble constant, changes with time. This isn't a puzzle, but is rather exactly what we expect. To understand this, let's look at it from the other point of view: theoretically.

A photo of me at the American Astronomical Society's hyperwall in 2017, along with the first Friedmann equation at right.Perimeter Institute / Harley Thronson

The first Friedmann equation is what you arrive at if you start with a Universe that's uniformly filled with matter, radiation, and whatever other forms of energy you want. The only assumptions are that the Universe is isotropic (the same in all directions), homogeneous (with the same average density everywhere), and governed by General Relativity. If you assume this, you get a relation between H, the Hubble rate (on the left-hand side), and all the various forms of matter and energy in the Universe (on the right-hand side).

The first Friedmann equation, as conventionally written today (in modern notation), where the left side details the Hubble expansion rate and the evolution of spacetime, and the right side includes all the different forms of matter and energy, along with spatial curvature.LaTeX / public domain

Interestingly, as your Universe expands, the density of matter, radiation, and energy are allowed to change. For example, as your Universe expands, its volume increases, but the total number of particles within your Universe stays the same. This means that, in an expanding Universe, for:

matter, its density drops as a-3,

radiation, its density drops as a-4,

and for dark energy, its density remains constant, evolving as a0,

where a is the scale factor (a proxy for the distance or the radius) of the Universe. As time goes on, a grows, and therefore different components of the Universe become more-or-less important relative to one another.

How matter (top), radiation (middle), and a cosmological constant (bottom) all evolve with time in an expanding Universe.E. Siegel / Beyond The Galaxy

A Universe with a greater overall energy density has a greater expansion rate. On the contrary, one with a smaller energy density has a lower expansion rate. As the Universe ages, it expands; as it expands, the matter and radiation within it becomes less dense; as it becomes less dense, the expansion rate drops. The expansion rate, at any given time, determines the value of the Hubble constant. In the distant past, the expansion rate was much larger, while today it's the smallest it's ever been.

Various components of and contributors to the Universe's energy density, and when they might dominate. If cosmic strings or domain walls existed in any appreciable amount, they'd contribute significantly to the expansion of the Universe. There could even be additional components that we no longer see, or that haven't appeared yet! Note that by time we reach today, dark energy dominates, matter is still somewhat important, but radiation is negligible.E. Siegel / Beyond The Galaxy

So why, then, you might wonder, do the very distant galaxies we observe appear to follow this straight-line relation? It's because all of the light that arrives at our eyes, from the light that was emitted by a galaxy next door to the light that was emitted from a galaxy billions of light years away, is all 13.8 billion years old by time it reaches us. The age of everything in the Universe, by time it reaches us today, has lived through the same ever-changing Universe that we have. The Hubble constant was higher in the distant past, when much of the light was emitted, but it's taken billions of years for that light to arrive at our eyes.

Light may be emitted at a particular wavelength, but the expansion of the Universe will stretch it as it travels. Light emitted in the ultraviolet will be shifted all the way into the infrared when considering a galaxy whose light arrives from 13.4 billion years ago.Larry McNish of RASC Calgary Center

Over that time, the Universe has expanded, meaning that the wavelength of that light has stretched. Only over the past 6 billion years or so has dark energy become important, and we've now reached the time where it's fast becoming the only component of the Universe that has an impact on our expansion rate. If we went back to a time when the Universe was half its present age, the expansion rate was 80% greater than it is today. When the Universe was just 10% of its current age, the expansion rate was 17 times greater than its present value.

But when the Universe reaches 10 times its current age, the expansion rate will only be 18% smaller than it is today.

The blue "shading" represent the possible uncertainties in how the dark energy density was/will be different in the past and future. The data points to a true cosmological "constant," but other possibilities are still allowed. Unfortunately, the conversion of matter into radiation cannot mimic dark energy; it can only cause what was once behaving as matter to now behave as radiation.Quantum Stories

This is due to the presence of dark energy, which behaves as a cosmological constant. In the far future, matter and radiation will both become relatively unimportant compared to dark energy, meaning that the Universe's energy density will remain constant. Under these circumstances, the expansion rate will reach a steady, finite value and stay there. As we move into the far future, the Hubble constant will become a constant not only in space, but in time as well.

In the far future, by measuring the velocity and distance to all the objects we can see, we'd get the same slope for that line everywhere. The Hubble constant will truly become a constant.

The relative importance of different energy components in the Universe at various times in the past. Note that when dark energy reaches a number near 100% in the future, the energy density of the Universe will remain constant arbitrarily far ahead in time.E. Siegel

If astronomers were more careful about their words, they would have called H the Hubble parameter, rather than the Hubble constant, since it changes over time. But for generations, the only distances we could measure were close enough that H appeared to be constant, and we've never updated this. Instead, we have to be careful to note that H is a function of time, and only today — where we call it H0— is it a constant. In reality, the Hubble parameter changes over time, and it's only a constant everywhere in space. Yet if we lived far enough in the future, we'd see that H stops changing entirely. As careful as we can be to make the distinction between what's actually constant and what changes now, in the far future, dark energy ensures there will be no difference at all.

I am a Ph.D. astrophysicist, author, and science communicator, who professes physics and astronomy at various colleges. I have won numerous awards for science writing since 2008 for my blog, Starts With A Bang, inclu...